A charter is a document listing the rights, duties and obligations of an executive or legislative body. In most cases, a governmental or quasi-governmental charter will specifically state under what authority the rights and duties are granted. For example, a King would grant a charter to commence exploration and ultimately colonization of a new island.
Charter schools are schools that have the "grant" of governmental authority to run somewhat independently of standard rules to better serve particular communities or interests such as public religious schools, schools that focus specifically on the arts or sciences, or schools that focus on special educational needs (such as public schools for the blind or for developmentally disabled students).
Many conservatives have used the more "liberal" idea of charter schools in arguing for the establishment of Christian schools in the public school system. New York city has funded several Christian charter schools along with one Islamic charter school and one Jewish charter schools.